Autism (ASD) and Attention Deficit/Hyperactivity Disorder (ADHD) are frequently observed in children, but are still not fully understood.
We want to investigate the overall association between social deficits and motor skills for each diagnosis group.
| Primary | Count | Avg Age | Males | Females | RightHanded | LeftHanded |
|---|---|---|---|---|---|---|
| ASD | 138 | 10.236 | 116 | 22 | 124 | 20 |
| ADHD | 176 | 9.6908 | 124 | 52 | 285 | 36 |
| TD | 254 | 10.2146 | 185 | 69 | 307 | 42 |
\[ \text{E[Social Deficit Score]} = \textbf{X} * \boldsymbol{\beta} \\ where: \\ \boldsymbol{\beta} = \begin{bmatrix} \text{Intercept} \\ \text{Balance Score} \\ \text{Aiming And Catching Score} \\ \text{EdinburgHandedness_Integer} \\ \text{GAI} \\ \text{Gender Male} \\ \text{mABC_AGE} \end{bmatrix} \]
\[ H_0: \text{Mean of SRS Total Scores from Version 1 = Mean of SRS Total Scores from Version 2} \\ H_1: \text{Mean of SRS Total Scores from Version 1} \space \neq \text{Mean of SRS Total Scores from Version 2} \\ \text{Under the null we got a t-statistc of -6.03 from a t-distribution of 417.38 Degrees of Freedom} \\ \text{that has a p-value of} \space 3.511 \times 10^{-9} \\ \space \text{Under} \space \alpha = .05 \space \text{we reject the null} \text{ and believe that there is a true difference in the mean} \]
##
## Call:
## lm(formula = SRS_TotalRawScore ~ mABC_AimingAndCatching.Component.StandardScore +
## mABC_Balance.Component.StandardScore + EdinburghHandedness_Integer +
## GAI + Gender + mABC_AGE, data = nodia2)
##
## Residuals:
## Min 1Q Median 3Q Max
## -6.9465 -2.7041 -0.5293 1.5000 18.0316
##
## Coefficients:
## Estimate Std. Error t value
## (Intercept) 43.52523 4.62720 9.406
## mABC_AimingAndCatching.Component.StandardScore 0.01693 0.19383 0.087
## mABC_Balance.Component.StandardScore -0.14406 0.16893 -0.853
## EdinburghHandedness_Integer -1.46571 1.07791 -1.360
## GAI 0.05956 0.03199 1.862
## GenderM -1.12175 1.24382 -0.902
## mABC_AGE -0.09471 0.42545 -0.223
## Pr(>|t|)
## (Intercept) 1.55e-15 ***
## mABC_AimingAndCatching.Component.StandardScore 0.9306
## mABC_Balance.Component.StandardScore 0.3958
## EdinburghHandedness_Integer 0.1769
## GAI 0.0655 .
## GenderM 0.3692
## mABC_AGE 0.8243
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 4.727 on 103 degrees of freedom
## (1 observation deleted due to missingness)
## Multiple R-squared: 0.06594, Adjusted R-squared: 0.01153
## F-statistic: 1.212 on 6 and 103 DF, p-value: 0.3062
\[ \boldsymbol{\beta} = \begin{bmatrix} \text{Intercept} \\ \text{Balance Score} \\ \text{Aiming And Catching Score} \\ \text{EdinburgHandedness_Integer} \\ \text{GAI} \\ \text{ADHD Subtype Inattentive} \\ \text{Gender Male} \\ \text{mABC_AGE} \end{bmatrix} = \begin{bmatrix} 64.0176 \\ -2.3512 \\ 1.3089 \\ 8.3848 \\ 0.0620 \\ -13.9720 \\ -9.3211 \\ -1.1236 \end{bmatrix} \]
## Analysis of Variance Table
##
## Model 1: SRS_TotalRawScore ~ mABC_AimingAndCatching.Component.StandardScore +
## mABC_Balance.Component.StandardScore
## Model 2: SRS_TotalRawScore ~ mABC_AimingAndCatching.Component.StandardScore +
## mABC_Balance.Component.StandardScore + EdinburghHandedness_Integer +
## GAI + ADHD_Subtype + Gender + mABC_AGE
## Res.Df RSS Df Sum of Sq F Pr(>F)
## 1 90 32488
## 2 85 25962 5 6526.4 4.2735 0.001626 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
\[ H_0: \text{Just Balance and Catching is Sufficient} \\ H_1: \text{Full Model is Sufficient} \\ \text{Under the null we got an F-statistic of 4.2735 where} \ F \sim F_{5,85} \\ \text{which gives us a p-value of .0016 with an} \ \alpha = .05 \ \text{we reject the null} \\ \text{and believe that we should keep every coefficient in the full model} \]
\[ \boldsymbol{\beta} = \begin{bmatrix} \text{Intercept} \\ \text{Balance Score} \\ \text{Aiming And Catching Score} \\ \text{EdinburgHandedness_Integer} \\ \text{GAI} \\ \text{ADHD Subtype Inattentive} \\ \text{Gender Male} \\ \text{mABC_AGE} \end{bmatrix} = \begin{bmatrix} 54.637 \\ 0.2525 \\ -0.9143 \\ 0.4960 \\ 0.0037 \\ -8.7537 \\ 1.6450 \\ 0.5879 \end{bmatrix} \]
## Analysis of Variance Table
##
## Model 1: SRS_TotalRawScore ~ mABC_AimingAndCatching.Component.StandardScore +
## mABC_Balance.Component.StandardScore
## Model 2: SRS_TotalRawScore ~ mABC_AimingAndCatching.Component.StandardScore +
## mABC_Balance.Component.StandardScore + EdinburghHandedness_Integer +
## GAI + ADHD_Subtype + Gender + mABC_AGE
## Res.Df RSS Df Sum of Sq F Pr(>F)
## 1 77 4764.4
## 2 72 4027.4 5 736.99 2.6351 0.03034 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
\[ H_0: \text{Just Balance and Catching is Sufficient} \\ H_1: \text{Full Model is Sufficient} \\ \text{Under the null we got an F-statistic of 2.6351 where} \ F \sim F_{5,72} \\ \text{which gives us a p-value of .03 with an} \ \alpha = .05 \ \text{we reject the null} \\ \text{and believe that we should keep every coefficient in the full model} \]
\[ \boldsymbol{\beta} = \begin{bmatrix} \text{Intercept} \\ \text{Balance Score} \\ \text{Aiming And Catching Score} \\ \text{EdinburgHandedness_Integer} \\ \text{GAI} \\ \text{Secondary Diagnosis Yes} \\ \text{Gender Male} \\ \text{mABC_AGE} \end{bmatrix} = \begin{bmatrix} 89.60022 \\ 0.47326 \\ -2.28800 \\ 13.96288 \\ -0.01026 \\ 1.25663 \\ 0.45815 \\ 0.87001 \end{bmatrix} \]
\[ \boldsymbol{\beta} = \begin{bmatrix} \text{Intercept} \\ \text{Balance Score} \\ \text{Aiming And Catching Score} \\ \text{EdinburgHandedness_Integer} \\ \text{GAI} \\ \text{Secondary Diagnosis Yes} \\ \text{Gender Male} \\ \text{mABC_AGE} \end{bmatrix} = \begin{bmatrix} 58.690482 \\ 0.179097 \\ 0.767967 \\ -2.043116 \\ 0.113743 \\ 8.627154 \\ -4.782354 \\ 0.002163 \end{bmatrix} \]